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Now on to quantum numbers…. Quantum Numbers PRINCIPAL: n energy level, the distance the orbital is from the nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l.

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Presentation on theme: "Now on to quantum numbers…. Quantum Numbers PRINCIPAL: n energy level, the distance the orbital is from the nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l."— Presentation transcript:

1 Now on to quantum numbers…

2 Quantum Numbers PRINCIPAL: n energy level, the distance the orbital is from the nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: m l spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: m s spin (+1/2 or -1/2)

3 Review Atomic number = # electrons Electrons occupy orbitals defined by n, l, m Each orbital can hold two electrons Orbitals  diffuse electron cloud “lower energy electron”  closer to nucleus Outer electrons: “valence” most reactive

4 The principal quantum number has the symbol n. n = 1, 2, 3, 4, “ shells ” (n = K, L, M, N,......) The electron ’ s energy depends principally on n. Quantum Numbers 1 2 3

5 Quantum Numbers The angular momentum quantum number has the symbol. = 0, 1, 2, 3, 4, 5, (n-1) = s, p, d, f, g, h, (n-1) tells us the shape of the orbitals. These orbitals are the volume around the atom that the electrons occupy 90-95% of the time.

6 Quantum Numbers The symbol for the magnetic quantum number is m, representing the spatial orientation. m = -, (- + 1), (- +2),.....0, , ( -2), ( -1), If = 0 (or an s orbital), then m = 0. If = 1 (or a p orbital), then m = -1,0,+1. x y z

7 If = 2 (or a d orbital), then m = -2,-1,0,+1,+2. If = 3 (or an f orbital), then m = -3,-2,- 1,0,+1,+2, +3. Theoretically, this series continues on to g,h,i, etc

8 Spin quantum number The last quantum number is the spin quantum number which has the symbol m s. The spin quantum number only has two possible values. –m s = +1/2 or -1/2

9 Spin of electron

10 Spin quantum number effects: –Every orbital can hold up to two electrons. Consequence of the Pauli Exclusion Principle. –The two electrons are designated as having –one spin up  and one spin down   Spin describes the direction of the electron’s magnetic fields.

11 Re-Cap: Quantum Numbers PRINCIPAL: n energy level, distance from nucleus (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: m l spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: m s spin (+1/2 or -1/2)

12 Atomic Orbitals: s, p, d, f Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. s orbital properties: –There is one s orbital per n level. = 0 and only one value of m = 0

13 s orbitals are spherically symmetric For every s orbital: = 0 and m l = 0 The only thing that changes for s orbitals is n.

14 1s orbital of hydrogen Distance from nucleus

15 Probability densities for finding an electron at a given radius 1s, 2s, and 3s orbitals for hydrogen

16 Three dimensional depictions of electron distribution

17 p orbital properties: –The first p orbitals appear in the n = 2 shell. p orbitals are peanut or dumbbell shaped volumes. There are 3 p orbitals per n level. –The three orbitals are named p x, p y, p z. = 1 for all p orbitals. m = -1,0,+1 (designate the three orientations) p orbitals

18 p orbitals are peanut or dumbbell shaped. l = 1

19 p orbitals are peanut or dumbbell shaped. l = 1 m = -1,0,+1

20 2p orbital

21 d orbital properties: –The first d orbitals appear in the n = 3 shell. The five d orbitals have two different shapes: –4 are clover leaf shaped. –1 is peanut shaped with a doughnut around it. –The orbitals lie directly on the Cartesian axes or are rotated 45 o from the axes. There are 5 d orbitals per n level. – The five orbitals are named: – They have an = 2. – m = -2,-1,0,+1,+2 (5 values of m )

22 = 2 m = -2,- 1,0,+1,+2

23 d orbital shapes = 2 m = -2,- 1,0,+1,+2

24 f orbital properties: –The first f orbitals appear in the n = 4 shell. The f orbitals have the most complex shapes. There are seven f orbitals per n level. –The f orbitals have complicated names. –They have an = 3 –m = -3,-2,-1,0,+1,+2, +3 7 values

25 = 3 m = -3,-2,-1,0,+1,+2, +3 7 values

26 f orbital shapes

27 Quantum Numbers PRINCIPAL: n energy level, distance from orbital (1, 2, 3, 4…) ANGULAR MOMENTUM: l shape (s = 0, p = 1, d = 2, f = 3) MAGNETIC: m l spatial orientation (0 for s; -1, 0, +1 for p; -2, -1, 0, +1, +2 for d, etc.) SPIN: m s spin (+1/2 or -1/2)

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29 only s s and p s, p and d

30 Recall that Shrodinger’s equations derives the orbitals!

31 s, p, and d shells of a hydrogen atom

32 Pauli Exclusion Principle –No two electrons in an atom can have the same set of 4 quantum numbers.

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34 The Aufbau Principle describes the electron filling order in atoms.

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36 paired parallel spins

37 Electron Configurations

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44 The order of orbital levels is: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s ….. Know configurations up to Ba!

45 Electron Configurations

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48 2.Or you can use the periodic chart

49 Ge = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 2 or [Ar] 4s 2 3d 10 4p 2 or [Ar]3d 10 4s 2 4p 2 Ge

50 Hund’s rule tells us that the electrons will fill the p orbitals by placing electrons in each orbital singly and with same spin until half-filled. Then the electrons will pair to finish the p orbitals.

51 3 rd row elements

52 Fourth row

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56 Specific quantum numbers for each electron

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58 How to deal with ions? S vs S 2- Cl vs Cl +

59 What type of ion would be expected to be favored for each element? Na Na + or Na - FF + or F - What are the electron configurations of the two C isotopes? 12 C 13 C

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61 Chemical properties  Valence electrons


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